I don't know if this is feasible, but I have a very small 40mm fan which is rated at 12 V/0.07 A, and the Arduino really can't run it with 5 volts. I plugged it into a 9 volt battery and the power worked great.

How would I go about adding around 9 volts for the fan while still letting the board control the power (this is a temperature control system for my BBQ smoker with thermistors. )

FYI. Those small 9V batteries are lousy at running motors (like fans). It'll only last 4 or 5 hours if the fan draws 50mA (de-rating since you aren't running at 12V). You'll want to use a AC to DC 9V supply.

My late father-in-law often mentioned a steam driven bbq spit design that he saw decades ago in a magazine (PM or similar I suppose). Alas he could never produce the design but was adamant that he had seen it, probably back in the 50s or so.

Since this is for a bbq, you could rig some kind of steam powered generator with the boiler tubes in the coals.....